Home
Class 12
MATHS
Find the volume of the larges cylinde...

Find the volume of the larges cylinder that can be inscribed in a sphere of radius `r`

Text Solution

Verified by Experts

The correct Answer is:
`(32pir^(3))/(81)`
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Objective Type Questions (A. Multiple Choice Questions)|45 Videos
  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise Objective Type Questions (B. Fill in the Blanks)|10 Videos
  • APPLICATIONS OF DERIVATIVES

    MODERN PUBLICATION|Exercise EXERCISE 1 (f) (Long Answer Type Questions (I))|24 Videos
  • APPLICATIONS OF THE INTEGRALS

    MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos

Similar Questions

Explore conceptually related problems

Prove that the volume of the largest cone that can be inscribed in a sphere of radius R is (8)/(27) of the volume of the sphere.

Prove that the volume of the largest cone,that can be inscribed in a sphere of radius R. is (8)/(27) of the volume of the sphere.

Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5sqrt(3)cm is 500 pi cm^(3).

Show that the maximum volume of the cylinder which can be inscribed in a sphere of radius 5sqrt(3)cm is 500 pi cm^(3).

The height of the cylinder of the greatest volume that can be inscribed in a sphere of radius 3 is

Show that the cone of greatest volume which can be inscribed in a given sphere is such that three times its altitude is twice the diameter of the sphere. Find the volume of the largest come inscribed ina sphere of radius R.

The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius =sqrt(3) is :

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is 2(R)/(sqrt(3)) .Also find maximum volume.

Show that the height of the cylinder of maximum volume that can be inscribed in a sphere of radius R is (2R)/(sqrt(3)) Also find the maximum volume.

MODERN PUBLICATION-APPLICATIONS OF DERIVATIVES-EXERCISE 1 (f) (Long Answer Type Questions (II))
  1. Show that the volume of the greatest cylinder, which can be inscribed ...

    Text Solution

    |

  2. Show that the altitude of the right circulau cone of maximum volume th...

    Text Solution

    |

  3. Find the volume of the larges cylinder that can be inscribed in a s...

    Text Solution

    |

  4. Find the volume of the larges cylinder that can be inscribed in a s...

    Text Solution

    |

  5. Show that the right-circular cone of least curved surface and given...

    Text Solution

    |

  6. Show that the height of the cylinder of maximum volume that can be in...

    Text Solution

    |

  7. Find the height of right circular cylinder of maximum volume that can ...

    Text Solution

    |

  8. Show that the radius of right - circular cylinder of maximum volume, t...

    Text Solution

    |

  9. Prove that the radius of the right circular cylinder of greatest cu...

    Text Solution

    |

  10. Of all the closed cylinderical cans (right - circular), which enclose ...

    Text Solution

    |

  11. Show that the surface area of a closed cuboid with square base and ...

    Text Solution

    |

  12. A figure consists of a semi-circle with a rectangle on its diameter...

    Text Solution

    |

  13. A window is the in the form of a reactangle, surmounted by a semi - ci...

    Text Solution

    |

  14. Show that a cylinder of a given volume which is open at the top has...

    Text Solution

    |

  15. The height of a closed cylinder of given volume and the minimum sur...

    Text Solution

    |

  16. Rectangles are inscribed inside a semicircle of radius r. Find the r...

    Text Solution

    |

  17. A square-based tank of capacity 250 cu m has to bedug out. The cost of...

    Text Solution

    |

  18. A tank with rectangular base and rectangular sides, open at the top...

    Text Solution

    |

  19. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box ...

    Text Solution

    |

  20. An open box is to be made of square sheet of tin with side 20 cm, by c...

    Text Solution

    |